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Variable-geometry structures are useful in aerospace applications because they are deployable, from a compact configuration (launch phase) to a spread geometry (operational phase). They may also benefit from the use of flexible joints, which store elastic energy for automatic deployment. Following the development of a self-deploying antenna frame structure with scissors, the geometrical configuration of a new kind of structure, simpler, lighter, and minimizing mechanical joints between elements, is proposed in this article. This topology can form a three-dimensional structure when partially opened or a planar structure when fully deployed. The applications concern autotensioning structures such as meshed space antenna, deorbiting sails, and also solar panel support structures.

The variable-geometry structures are useful in the aerospace applications because they cross of a compact configuration (launch phase) in a spread geometry (operational phase). Due to its expertise on the conception of light weight structures, the SIGECO team designs and realizes innovative structures: their advantage is to deploy automatically by storage of energy of flexion in flexible joints. A first study was led on a structure with scissors which conceive the skeleton of an auto-deployable satellite antenna. Following upon these works, the aim of this article is to propose the geometrical configuration of another kind of structure without articulations between elements (pivots, slide junctions). This structure form a circular plane or a three-dimensional structure (partially opened). The bar number is divided by two compared to the scissor. The applications concern auto-tensing structures as space antenna (LDR or other), desorbitation or solar sails and stiff structures for the support of solar panels.

Previous studies have addressed why and how mono‐stratified epithelia adopt a polygonal topology. One major additional, and yet unanswered question is how the frequency of different cell shapes is achieved and whether the same distribution applies between non-prolifer-ative and proliferative epithelia. We compared different proliferative and non-proliferative epithelia from a range of organisms as well as Drosophila melanogaster mutants, deficient for apoptosis or hyperproliferative. We show that the distribution of cell shapes in non‐prolif-erative epithelia (follicular cells of five species of tunicates) is distinctly, and more stringently organized than proliferative ones (cultured epithelial cells and Drosophila melanogaster imaginal discs). The discrepancy is not supported by geometrical constraints (spherical versus flat monolayers), number of cells, or apoptosis events. We have developed a theoretical model of epithelial morphogenesis, based on the physics of divided media, that takes into account biological parameters such as cell‐cell contact adhesions and tensions, cell and tissue growth, and which reproduces the effects of proliferation by increasing the topological heterogeneity observed experimentally. We therefore present a model for the morphogene-sis of epithelia where, in a proliferative context, an extended distribution of cell shapes (range of 4 to 10 neighbors per cell) contrasts with the narrower range of 5-7 neighbors per cell that characterizes non proliferative epithelia.

A new conceptual design for the architecture of a large deployable space reflector is presented. The reflective parabolic surface is made of a mesh shaped by a cable net and the supporting rim structure is based on scissor mechanisms associated with flexible joints. These joints replace complex articulations while allowing the storage of the energy required for deployment. They also affect the stiffness of the structure and the tension of the cable net. The dynamic behavior was studied by finite element modeling and through tests on an experimental prototype with a gravity compensation device. We focused on the first natural mode, which is an important design criterion for space applications. The measurements are compared to simulation results and we discuss the influence of suspension threads and gravity in the model.

Tissue morphogenesis is a key point remaining weakly understood in development biology. Indeed, most of plants or animals epithelial tissues show analogous cell polygonal distributions.Accordingly, one may think of invariant features governing this process.We propose an original 2D-model based on divided media to explore the potential role of mechanics in epithelial morphogenesis. A cell is represented by repulsive “cytoplasm-grains”maintained inside a closed membrane composed of “membrane-gains” connected via “membrane-tendons”. We consider different substrate geometries: a sphere, to mimick Ciona Intestinaliseggs and a plane, as for culture boxes. The evolution through time is simulated using the molecular dynamics approach where cell growth, division and apoptosis are computed to simulatethe formation of tissues following two mechanisms: (i) accretion and (ii) proliferation.In the accretion scenario, the sphere and the cells grow while new small cells are inserted randomly. Thus, the growth parameters are related to the arrival of new cells and the size of thecells and of the spherical egg.In the proliferative scenario, the tissue takes form by growing of cells and afterwards dividing into child cells, and/or dying (apoptosis). It is governed by the ratio between the number ofapoptosis and of mitoses, defined as the “proliferation rate”.The numerical results obtained following the two scenarii reproduce the experimental observations. This indicates that mechanical interactions could play a major role in tissue formation. Atthe opposite, both the substrate geometry and boundary conditions do not significantly influence cell geometry, what was hardly foreseeable.In the accretion scenario, the number of hexagonal cells and the standard deviations for the polygonal distributions decrease slightly as the tissue formation rate decreases: a slowerdevelopment speed could allow the cells to pack better during their reorganization and growth, resulting in a more reproductible topology. Otherwise, the number of hexagonal cells obtainedfor each accretion scenario is always higher than with the proliferative one, which may be attributed to the disruptive role of cell division in tissue reorganization.In the proliferation scenario, the numerical distributions get closer to experimental observations when the proliferation rate increases. In parallel, the corresponding standard deviationsdecrease. Accordingly, apoptosis may play a crucial role in tissue morphogenesis regulation by counterbalancing the plausible disruptive effect of cell division.In spite of its oversimplification, this promising approach based on an original cell-tissue modelling may allow new useful architectural descriptions and mechanical analysis in epithelialmorphogenesis.